|Publication number||US7392139 B2|
|Application number||US 11/389,228|
|Publication date||Jun 24, 2008|
|Filing date||Mar 27, 2006|
|Priority date||Mar 27, 2006|
|Also published as||EP1999488A1, EP1999488B1, US20070225917, WO2007109913A1|
|Publication number||11389228, 389228, US 7392139 B2, US 7392139B2, US-B2-7392139, US7392139 B2, US7392139B2|
|Inventors||Maria Giovanna Guatteri|
|Original Assignee||Swiss Reinsurance Company|
|Export Citation||BiBTeX, EndNote, RefMan|
|Patent Citations (10), Non-Patent Citations (3), Classifications (6), Legal Events (4)|
|External Links: USPTO, USPTO Assignment, Espacenet|
The present invention relates to a system and a method for providing earthquake data. Specifically, the present invention relates to a computer system and a computer-implemented method for providing earthquake data for a defined area.
Despite many advances in seismology and although many attempts have been made by seismologists and others to create systems for earthquake predictions, many experts do not believe that a system for predicting effectively and precisely individual earthquakes would be possible. However, more general forecasts, estimating the likelihood of an earthquake of a particular magnitude affecting a particular location within a particular time span, are used to establish seismic hazard. Furthermore, for various purposes, it is desirable to determine how specific geographical areas will be affected by earthquakes over a defined length of time. This determination of long term earthquake data is particularly useful for controlling earthquake simulators, e.g. earthquake simulators that are fully computer-implemented, showing representations of earthquake events on a display, or earthquake simulators that comprise motion drivers that move mechanically parts of a model of a geographic area. Moreover, the determination of long term earthquake data is useful for generating stochastic earthquake event sets for application in loss estimation tools, used, for example, in the insurance and reinsurance industry, or for structuring pure parametric catastrophe bond deals.
It is an object of this invention to provide a computer system and a computer-implemented method for providing earthquake data for a defined geographical area and for seismic activity over a defined length of time. In particular, it is an object of the present invention to provide a computer system and a computer-implemented method for providing earthquake data wherein, on one hand, the earthquake data is consistent with historical data, and wherein, on the other hand, the earthquake data is not biased by the historical data to such an extent that randomness is no longer accounted for. It is a further object of the present invention to provide a computer system and a computer-implemented method for providing earthquake data wherein a potentially high number of earthquake events occurring in the defined length of time is reflected and handled accurately, while computer limitations and computational constraints are met (e.g. limitations on memory, processing speed and time).
According to the present invention, these objects are achieved particularly through the features of the independent claims. In addition, further advantageous embodiments follow from the dependent claims and the description.
According to the present invention, the above-mentioned objects are particularly achieved in that, for providing earthquake data for a defined area, stored in a first data store are locations of a plurality of earthquake epicenters; stored in a second data store are seismic parameters associated with a plurality of seismic zones, the seismic parameters being indicative at least of magnitude and likelihood of earthquakes in each of the seismic zones; determined from the first data store is a location of a selected epicenter within the area, e.g. by using bootstrap sampling; determined from the second data store is a selected magnitude associated with a selected seismic zone comprising the selected epicenter; established are characteristics of a plurality of earthquake events in the area over a defined length of time, the characteristics of an earthquake event including at least a selected epicenter and a selected magnitude; and generated is a signal indicative of the characteristics of the earthquake events. Defining earthquake events by determining their epicenters from a data store with historic epicenters and by determining their magnitudes from a data store with seismic parameters make possible an easy to maintain earthquake hazard model with flexible and simple parameterization. This earthquake hazard model provides earthquake data consistent with historical data and relies on complete and stable magnitude sampling. An earthquake catalog that includes instrumental and/or historical data is used as the basis for the locations of earthquake epicenters. The generated (simulated) earthquake events have the same magnitude-frequency distribution as the earthquake catalog. Moreover, characteristic earthquakes are also included in the modeling. The seismicity in the historic catalog is reflected in a stochastic event set comprising a plurality of earthquake events. Seismic zones that showed a high seismicity in the past will also show high seismicity in the future. Because the relative concentration of epicenters in different areas is reflected automatically in the stochastic event set, the “a” value of the Gutenberg-Richter distribution does not need to be pre-computed. Thus the generation of the earthquake events is simplified without decreasing their (statistical) quality.
In an embodiment, the total number of different earthquake events to be determined is determined based on the length of time to be covered by the earthquake data and on the average number of earthquake events in the area in a recording period.
Preferably, the magnitude of earthquakes in the area is split into at least two ranges of higher and lower magnitudes, and the number of earthquake events to be determined is limited for ranges with lower magnitudes, while the frequency of these latter earthquake events is adjusted correspondingly. In other words, earthquakes of lower magnitudes are down sampled, and, to preserve the total magnitude-frequency distribution, the respective event frequencies are multiplied by the factor of down sampling. Thereby, a potentially high number of earthquake events occurring in the defined length of time is reflected and handled accurately, while computer limitations, e.g. memory space, and computational constraints, e.g. processing speed and time, are met.
Preferably, the seismic parameters define a Gutenberg-Richter distribution, and the selected magnitude is determined through random sampling, e.g. using stratified sampling, from the Gutenberg-Richter distribution defined by the seismic parameters associated with selected seismic zone. For example, the seismic parameters include cumulative numbers of earthquakes of given magnitudes per year in the seismic zones and/or return periods of earthquakes of specific magnitudes in the seismic zones.
Preferably, a selected location is determined by applying a spreading function to the location of the selected epicenter, and the selected location is used as the location of the selected epicenter. For example, the spreading function includes random sampling from a circular area centered in the location of the selected epicenter, the circular area having an epicenter density corresponding to the epicenter density in the selected seismic zone.
In an embodiment, the seismic parameters are further indicative of a depth of earthquakes in each of the seismic zones. Furthermore, a selected depth of the selected epicenter is determined through random sampling from a distribution of the depth associated with the selected seismic zone, and the selected depth is included in the characteristics of an earthquake event.
In various embodiments, shown on a display are representations of earthquake events based on the signal, controlled is an earthquake simulator using the signal, and/or stored are stochastic earthquake event sets based on the signal. For example, based on the stochastic earthquake event sets, loss values are estimated and/or parameters of a financial investment structure are defined.
In addition to a computer system and a computer-implemented method for providing earthquake data for a defined area, the present invention also relates to a computer program product including computer program code means for controlling one or more processors of a computer, such that the computer stores locations of a plurality of earthquake epicenters; stores seismic parameters associated with a plurality of seismic zones, the seismic parameters being indicative at least of magnitude and likelihood of earthquakes in each of the seismic zones; determines from the locations a location of a selected epicenter within the area; determines from the seismic parameters a selected magnitude associated with a selected seismic zone comprising the selected epicenter; establishes characteristics of a plurality of earthquake events in the area over a defined length of time, the characteristics of an earthquake event including at least a selected epicenter and a selected magnitude; and generates a signal indicative of the characteristics of the earthquake events. Particularly, the computer program product includes a computer readable medium containing therein the computer program code means.
The present invention will be explained in more detail, by way of example, with reference to the drawings in which:
As is illustrated in
The control module 10 is designed to control the individual functional modules as well as the user interface of computer system 1. The user interface is visualized on display 20 and receives data from the user through the data entry means of computer system 1.
As illustrated in
In step S2, defined and stored are set parameters for an earthquake event set that is to be generated.
In step S3, the characteristics of a plurality of earthquake events are established based on the input data, prepared in step S1, for the earthquake event set, defined in step S2.
In step S4, earthquake data is provided based on the characteristics of earthquake events established in step S3.
As illustrated in
In step S11, control module 10 stores the locations of the epicenters found in catalog 21 in the first data store 22. The control module 10 stores the locations of epicenters within a specific geographical area 4 or of all earthquakes stored in catalog 21. Preferably, only epicenters of earthquakes having a defined minimum magnitude exceeding a defined threshold magnitude, e.g. M>=3, are stored in the first data store 22.
In step S12, control module 10 stores definitions of the seismic zones in the second data store 23. For example, the seismic zones 41, 42, 43, 44, 45, 46 are defined by coordinates or zone identifiers (e.g. names) associated with coordinates. The seismic zones are defined for a specific geographical area 4 or for all the locations of the earthquake data stored in the first data store 22. Definitions of the seismic zones 41, 42, 43, 44, 45, 46 are received from data source 3 and/or through manual data entry from the user.
In step S13, control module 10 assigns to each seismic zone 41, 42, 43, 44, 45, 46 defined in the second data store 23 the seismic parameters associated with that zone. For the background seismic zones assigned are a “b” value, and a minimum and maximum magnitude that define the local Gutenberg-Richter distribution (magnitude-frequency distribution). For the characteristic seismic zones a return period and a characteristic magnitude are assigned. The user has also the option to assign a depth range. Attenuation parameters used to calculate the shaking intensity for each event are also assigned for each seismic zone 41, 42, 43, 44, 45, 46. The seismic parameters are received from data source 3 and/or through manual data entry from the user.
As illustrated in
In step S22, the control module 10 stores the length of time T, e.g. a time span of a number of years, for which the earthquake event set is to be determined (i.e. the duration of a synthetic earthquake catalog, in which each event has an event frequency of f=1/T). The length of time T is received from the user through manual data entry.
In step S23, the generator module 14 determines from the earthquake catalog 21 the average number of earthquake events in a given recording period in the geographic area 4, specified in step S21.
In step S24, the generator module 14 determines the total number of different earthquake events to be determined for the event set based on the length of time, specified in step S22, and the average number of earthquake events in the area, as determined in step S23. For example, if the earthquake catalog covers a recording period of 200 years since catalog completeness and includes 80 earthquakes greater than the threshold magnitude, an average number of 80 earthquakes occur every 200 years. Thus, if the length of time is set to 150,000 years, 60,000 events need to be generated for the event set. The basic assumption is that earthquakes are temporally independent.
As illustrated in
Preferably, the limiter module 15 limits the total number of simulated events for lower magnitude ranges (e.g. as part of step S24 or S34). This is achieved by splitting the overall magnitude range for the geographical area into two or more magnitude ranges. The magnitude threshold that controls the split is calculated as the quantile q of the magnitude cumulative distribution function corresponding to a given percentile value p, e.g. 95%. Generally, events corresponding to a percentile of 95% or less are small-moderate magnitude events. Over the lower range of magnitudes (below q), the number of simulated events is limited to Nmax and reducing the number of bootstrap sampling by a factor F. The factor F is calculated as Nmax divided by the number of events in the same magnitude range over the length of time T, specified in step S22. In order to preserve the total magnitude-frequency distribution, the corresponding event frequency is multiplied by the same factor F. For the magnitude range above q, there is no down sampling applied in order to preserve the stability of the simulation, as fewer events are generated for large magnitude.
In step S32, to account for randomness of earthquake locations, the placement module 11 applies an adaptive epicenter spreading function 12 to the epicenter location E selected in step S31. As is illustrated in the example of
In step S33, the placement module 11 selects the depth of the selected epicenter through empirical or random sampling, e.g. through random sampling from a depth distribution associated with the selected seismic zone 46. For example, the depth distribution is provided in the earthquake catalog 21 or specified as uniform distribution by the user.
In step S34, the severity module 13 determines in the second data store 23 the seismic zone 46 that comprises the selected epicenter E (or E′, respectively) and determines a magnitude associated with this seismic zone 46. The magnitude is determined by the severity module 13 through random sampling from a Gutenberg-Richter distribution, defined by seismic parameters associated with the seismic zone 46 and retrieved from the second data store 23. For example, the magnitude is determined using a stratified sampling technique or Latin Hypercube Sampling described in McKay, M. D., W. J. Conover and R. J. Beckman, “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code”, Technometrics 21: 239-245, 1979. In essence, the severity module 13 combines a Gutenberg-Richter model and a characteristic earthquake model to select (simulate) event magnitudes.
For background seismic (source) zones (e.g. for magnitude ranges below 7), the Gutenberg-Richter distribution, as noted below in equation (1), represents mathematically the empirical correlation that the number of earthquakes decreases with increasing magnitude.
log N(M)=a-bM (1)
Where N is the cumulative number of earthquakes (per year) with magnitude greater or equal than M. N can be considered as the mean annual rate of exceedance, λm, of a given magnitude m. The “a” and “b” parameters in equation (1) are generally obtained by regression on a database of recorded earthquakes in the source zone of interest. 10a is the mean yearly number of earthquakes of magnitude greater than or equal to zero. The “b” parameter describes the relative likelihood of large and small earthquakes. In a logarithmic plot the cumulative number of events is a linear function of magnitude with slope equal to the “b” parameter. It is to be noted, however, that in the present system 1 and method for providing earthquake data, the “a” value of the Gutenberg-Richter distribution does not need to be pre-computed, because the relative concentration of epicenters in different areas is reflected automatically in the stochastic event set.
For characteristic seismic (source) zones (e.g. for magnitude ranges above 7), a characteristic earthquake model assigns a specific return period to a specific magnitude, instead of deriving it from a Gutenberg-Richter distribution. The return period and characteristic magnitude are often derived from paleoseismology studies or from historical records that span a long time period. The frequency and magnitude assigned to characteristic events are subject to uncertainty, therefore a range of possible values are assigned to the characteristic frequency and/or magnitude. Usually, either a uniform or a Gaussian distribution is assumed to describe the characteristic magnitude. However, such an approach is not consistent with the observation that small events have more probability of occurrence than large events. Thus, in the present system 1 and method for providing earthquake data, the occurrence of characteristic earthquakes is modeled with an exponential distribution, such as the Gutenberg-Richter distribution, with a very low b-value in order to give enough weight to the large events. It is to be noted, that the term b-value in this context has nothing to do with historical seismicity. The characteristic return period is generated using a logNormal distribution with parameters taken from the literature and/or assigned by trial and error.
In step S35, the generator module 14 stores the characteristics of the earthquake event, the characteristics including the epicenter location E (or E′, respectively) as determined in steps S31 and S32, the depth as determined in step S33, and the magnitude as determined in step S34.
In step S36, the generator module 14 checks whether or not the earthquake characteristics have been established for the total number of events, as determined in step S24 (and possibly adjusted by the limiter module 15). If further events need to be determined, the generator module 14 proceeds in step S31. Otherwise, if the full number of events has been determined, the generator module 14 proceeds in step S4.
As illustrated in
In step S42, the simulator application module 18 controls dynamically a hardware based earthquake simulator 2 or a computer based earthquake simulator 19 based on the signal generated in step S41. For example, the simulator application 18 generates one or more control signals based on the signal generated in step S41 and provides this control signal to the earthquake simulator 2 or 19. Responsive to the control signal, the earthquake simulator 2, 19 generates dynamic simulations of a series of earthquake events represented graphically on display 20 or mechanically by motion drivers of earthquake simulator 2, respectively.
In step S43, the display application module 17 shows on display 20 a graphical representation of earthquake events based on the signal generated in step S41.
In step S44, the data application module 16 stores a stochastic earthquake event set based on the signal generated in step S41. In an embodiment, the computer system 1 further comprises a loss estimation module configured to estimate loss values based on the stochastic earthquake event set. In another embodiment, the computer system 1 further comprises a financial structuring module configured to define parameters of a financial investment structure based on the stochastic earthquake event sets.
The foregoing disclosure of the embodiments of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many variations and modifications of the embodiments described herein will be apparent to one of ordinary skill in the art in light of the above disclosure. The scope of the invention is to be defined only by the claims appended hereto, and by their equivalents. Specifically, in the description, the computer program code has been associated with specific software modules, one skilled in the art will understand, however, that the computer program code may be structured differently, without deviating from the scope of the invention. Moreover, in describing representative embodiments of the invention, the specification may have presented the method and/or process of the invention as a particular sequence of steps. However, to the extent that the method or process does not rely on the particular order of steps set forth herein, the method or process should not be limited to the particular sequence of steps described. As one of ordinary skill in the art would appreciate, other sequences of steps may be possible. Therefore, the particular order of the steps set forth in the specification should not be construed as limitations on the claims. In addition, the claims directed to the method and/or process of the invention should not be limited to the performance of their steps in the order written, and one skilled in the art can readily appreciate that the sequences may be varied and still remain within the spirit and scope of the invention.
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|U.S. Classification||702/15, 340/690|
|International Classification||G08B21/00, G06F19/00|
|Aug 28, 2006||AS||Assignment|
Owner name: SWISS REINSURANCE COMPANY, SWITZERLAND
Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:GUATTERI, MARIA GIOVANNA;REEL/FRAME:018246/0605
Effective date: 20060417
|Sep 28, 2011||AS||Assignment|
Owner name: SWISS REINSURANCE COMPANY LTD., SWITZERLAND
Free format text: CORPORATE NAME CORRECTION;ASSIGNOR:SWISS REINSURANCE COMPANY;REEL/FRAME:026982/0191
|Nov 30, 2011||FPAY||Fee payment|
Year of fee payment: 4
|Dec 9, 2015||FPAY||Fee payment|
Year of fee payment: 8